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We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schroedinger cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation.
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Dynamics of the double-well Bose-Einstein condensate subject to energy dissipation is studied by solving a reduced one-dimensional time-dependent Gross-Pitaevskii equation numerically. We first reproduce the phase space diagram of the system without dissipation systematically, and then calculate evolutionary trajectories of dissipated systems. It is clearly shown that the dissipation can drive the system to evolve gradually from the $pi$-mode quantum macroscopic self-trapping state, a state with relatively higher energy, to the lowest energy stationary state in which particles distribute equally in the two wells. The average phase and phase distribution in each well are discussed as well. We show that the phase distribution varies slowly in each well but may exhibit abrupt changes near the barrier. This sudden change occurs at the minimum position in particle density profile. We also note that the average phase in each well varies much faster with time than the phase difference between two wells.
In ultracold atomic gases, a unique interplay arises between phenomena known from condensed matter physics, few-body physics and chemistry. Similar to an electron in a solid, an impurity in an ultracold gas can get dressed by excitations from the medium, forming a quasiparticle called the polaron. We study how dressing of an impurity leads to a modification of its chemical reactivity. Using a Gaussian state variational method in the frame of the impurity, we demonstrate that three-body correlations lead to an instability of the polaron. This instability is connected to an Efimov resonance, but shifted to smaller interactions by many-body effects, showing that polaron formation stimulates Efimov physics and the associated chemistry.
We investigate a Bose-Einstein condensate in strong interaction with a single impurity particle. While this situation has received considerable interest in recent years, the regime of strong coupling remained inaccessible to most approaches due to an instability in Bogoliubov theory arising near the resonance. We present a nonlocal extension of Gross-Pitaevskii theory that is free of such divergences and does not require the use of the Born approximation in any of the interaction potentials. We find a new dynamical transition regime between attractive and repulsive polarons, where an interaction quench results in a finite number of coherent oscillations in the density profiles of the medium and in the contact parameter before equilibrium is reached.
We present the first experimental realisation of Bose-Einstein condensation in a purely magnetic double-well potential. This has been realised by combining a static Ioffe-Pritchard trap with a time orbiting potential (TOP). The double trap can be rapidly switched to a single harmonic trap of identical oscillation frequencies thus accelerating the two condensates towards each other. Furthermore, we show that time averaged potentials can be used as a means to control the radial confinement of the atoms. Manipulation of the radial confinement allows vortices and radial quadrupole oscillations to be excited.
We analyze the properties of an impurity in a dilute Bose-Einstein condensate (BEC). First the quasiparticle residue of a static impurity in an ideal BEC is shown to vanish with increasing particle number as a stretched exponential, leading to a bosonic orthogonality catastrophe. Then we introduce a variational ansatz, which recovers this exact result and describes the macroscopic dressing of the impurity including its back-action onto the BEC as well as boson-boson repulsion beyond the Bogoliubov approximation. This ansatz predicts that the orthogonality catastrophe also occurs for mobile impurities, whenever the BEC becomes ideal. Finally, we show that our ansatz agrees well with experimental results.
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